Related papers: Tree Contractions and Evolutionary Trees

By introducing the notions of living and dead nodes a new model of random tree evolution with continuous time parameter has been constructed. It is assumed that two random variables, the lifetime and the offspring number of living nodes…

A compacted binary tree is a directed acyclic graph encoding a binary tree in which common subtrees are factored and shared, such that they are represented only once. We show that the number of compacted binary trees of size $n$ grows…

Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…

Crossover and mutation are the two main operators that lead to new solutions in evolutionary approaches. In this article, a new method of performing the crossover phase is presented. The problem of choice is evolutionary decision tree…

When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in…

Evolution is a process that is influenced by various environmental factors, e.g. the interactions between different species, genes, and biogeographical properties. Hence, it is interesting to study the combined evolutionary history of…

Model trees provide an appealing way to perform interpretable machine learning for both classification and regression problems. In contrast to ``classic'' decision trees with constant values in their leaves, model trees can use linear…

Species trees represent the historical divergences of populations or species, while gene trees trace the ancestry of individual gene copies sampled within those populations. In cases involving rapid speciation, gene trees with topologies…

Phylogenetic (i.e. leaf-labeled) trees play a fundamental role in evolutionary research. A typical problem is to reconstruct such trees from data like DNA alignments (whose columns are often referred to as characters), and a simple…

Given two phylogenetic trees with the $\{1, \ldots, n\}$ leaf-set the maximum agreement subtree problem asks what is the maximum size of the subset $A \subseteq \{1, \ldots, n\}$ such that the two trees are equivalent when restricted to…

Phylogenetic trees are used to model evolution: leaves are labelled to represent contemporary species ("taxa") and interior vertices represent extinct ancestors. Informally, convex characters are measurements on the contemporary species in…

In this paper, we lay the groundwork on the comparison of phylogenetic networks based on edge contractions and expansions as edit operations, as originally proposed by Robinson and Foulds to compare trees. We prove that these operations…

Unrooted phylogenetic networks are graphs used to represent evolutionary relationships. Accurately reconstructing such networks is of great relevance for evolutionary biology. It has recently been conjectured that all phylogenetic networks…

Packing graphs is a combinatorial problem where several given graphs are being mapped into a common host graph such that every edge is used at most once. In the planar tree packing problem we are given two trees T1 and T2 on n vertices and…

Tree-based phylogenetic networks, which may be roughly defined as leaf-labeled networks built by adding arcs only between the original tree edges, have elegant properties for modeling evolutionary histories. We answer an open question of…

A transversal in a rooted tree is any set of nodes that meets every path from the root to a leaf. We let c(T,k) denote the number of transversals of size k in a rooted tree T. We define a partial order on the set of all rooted trees with n…

Trees are useful entities allowing to model data structures and hierarchical relationships in networked decision systems ubiquitously. An ordered tree is a rooted tree where the order of the subtrees (children) of a node is significant. In…

Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of $n$ variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the…

The Subtree Isomorphism problem asks whether a given tree is contained in another given tree. The problem is of fundamental importance and has been studied since the 1960s. For some variants, e.g., ordered trees, near-linear time algorithms…

Decision trees are popular machine learning models that are simple to build and easy to interpret. Even though algorithms to learn decision trees date back to almost 50 years, key properties affecting their generalization error are still…